Consider a manifold constructed by identifying the boundaries of Euclidean triangles or Euclidean tetrahedra. When these form a closed topological manifold, we call such spaces piecewise flatâ€¦ (More)

A combinatorial version of Yamabe flow is presented based on Euclidean triangulations coming from sphere packings. The evolution of curvature is then derived and shown to satisfy a heat equation. Theâ€¦ (More)

where i is the linear interpolation of f over the triangle Ti in T and the sum is over all triangles in the triangulation. One may consider changing the triangulation by exchanging two trianglesâ€¦ (More)

This article studies a discrete geometric structure on triangulated manifolds and an associated curvature flow (combinatorial Yamabe flow). The associated evolution of curvature appears to be like aâ€¦ (More)

Consider a sequence of pointed nâ€“dimensional complete Riemannian manifolds {(Mi, gi(t), Oi)} such that t âˆˆ [0, T ] are solutions to the Ricci flow and gi(t) have uniformly bounded curvatures andâ€¦ (More)

IEEE transactions on visualization and computerâ€¦

2018

Non-linear dimensionality reduction (NDR) methods such as LLE and t-SNE are popular with visualization researchers and experienced data analysts, but present serious problems of interpretation. Inâ€¦ (More)

In his proof of Andreevâ€™s theorem, Thurston in [18] introduced a conformal geometric structure on two dimensional simplicial complexes which is an analogue of a Riemannian metric. He then used aâ€¦ (More)

In his proof of Andreevâ€™s theorem, Thurston in [1] introduced a conformal geometric structure on two dimensional simplicial complexes which is an analogue of a Riemannian metric. He then used aâ€¦ (More)